How do you change the materials of linked instances stored in another blend file?
This is what worked for me.
I have two master blend files.  One containing the materials, which are specific to the product.  And another one of the product model.
When I create a new blend file to create a scene with the product using the materials, I need to be able to update the master files and see them update in the new blend file. For example, when I show the final scene to the client and they want you to make a tweak to one of the materials, or a tweak to the product model, I would be able to go to the master blend files, make the tweaks and any other blend file that is linked will automatically update.

This is how I set it up:
First I need to create a link to the model or material

Then I navigate to the master blend file for that model and import it.  Here I have the product saved as a collection, so I select the collection the model contains:

I repeat the same steps to import the materials, except this time I navigate to the materials folder inside the blend file and select all the materials I want to link:

Next I make sure the model is selected and while in Object Model I go to Object&gt;Relations&gt;Make Library Override and confirm:

Now I can access the materials panel, but in order to update the material to one of the linked materials I have to switch it from Data to Object:

Now if I click the icon to change the material, I now have access to my linked materials and can update the models material in the scene:

Now if I need to make a tweak to the material or model, I can open either of those master blend files, make the tweaks and save.  If I'm working with the current scene and master files and have two instances of Blender open, I can force an update by doing the following:
First I change the outliner from View Layer to Blend File:

I scroll the outliner to the bottom until I see the two linked files, indicated by the link chain icon.  I right click one of those and select reload.  Then it updates the scene to reveal the latest tweaks!